Page 37 - Read Online

Page 14 of 18 Liu et al. J. Mater. Inf. 2025, 5, 27 I http://dx.doi.org/10.20517/jmi.2024.105

Supplementary Figure 8. Although all of the reconstructed surfaces are less stable than the clean -Fe 2C(111)
surface, the energy differences between them are relatively small, especially for carbon-rich structures under a
high Δ C. For example, at the lower limit of Δ C = -7.45 eV, the most stable reconstructed surface is identified
as “-3C”. This means the surface energy is minimized when three fewer carbon atoms are present compared
to the unreconstructed structure. Conversely, at the upper limit of Δ C = -6.60 eV, the relative surface energy
decreases monotonically with an increasing carbon number. In the end, the stability of the surface with most
carbon atoms (“+C”) is very close to the clean surface. This suggests carbon deposition on the iron-carbon
surface is presumed to be thermodynamically favorable under a high Δ C, typically near the reactant-catalyst
equilibrium in a carbon-rich gas environment.

CONCLUSIONS
To summarize, we have constructed the FT DP model by fine-tuning the DPA-2 LAM on a dataset focused on
2
the iron-based FTS process and demonstrating its performances for the investigation of key reaction pathways
in the FTS process and global optimization of several iron carbide surfaces with edge sites. The model valida-
tion and the atomistic simulation tasks served as comparative analysis between the results obtained through
MLP and DFT calculations demonstrate that our FT DP fine-tuning protocol exhibits significant promise for
2
constructing universal MLPs with notable performance in studying reaction pathways, surface reconstruction
and other atomistic processes of complex heterogeneous catalytic systems such as iron-based FTS, providing
a valuable practice for the application of LAM in the theoretical simulation of heterogeneous catalysis as well.
It should be emphasized that all our works including DFT calculation, MLP training, and atomic simulation
workflowconstructionhavebeenconductedinopen-sourceplatformsforintegratingthecollectiveintelligence
of developers from varying domains and making our contributions at the same time.

We close the paper by giving a few general remarks. While the FT DP model constructed via our fine-tuning
2
protocol has achieved promising results, there remains significant room for improvement. Most importantly,
since the model is pre-trained and fine-tuned by mainly using DFT data at the GGA-level, it is expected to
be inadequate for systems with strong electronic correlation such as the surfaces of Fe oxides that also play
important roles in the FTS process. To extend the FT DP model to more diverse chemical scenarios that are
2
relevant to FTS, it is necessary to include more accurate DFT training data that cover structures falling outside
the current training set. First-principles calculation of strongly correlated materials with sufficient accuracy
and efficiency is challenging by itself, and it is under active exploration to build unified MLP models that can
describe weakly and strongly correlated systems with comparable accuracy by using mixed training data ob-
tained from different theoretical methods. Considering highly demanding computational cost of generating
new training data, especially when using advanced electronic structure methods beyond GGA that are nec-
essary for strongly correlated systems, it is crucial to leverage various active learning strategies [70] to discern
iteratively and automatically unlabeled structures that can improve the current model in the most efficient way.
There are available platforms to facilitate this process such as DP-GEN [37] ; however, further optimizing the
active learning protocol for fine-tuned LAMs remains an open challenge. For example, conventional data se-
lection criteria in active learning often rely on ensemble-based (also known as query-by-committee [70] ) uncer-
tainty quantification, which may under-perform for LAMs owing to additional computational costs required
for training several large models, and more importantly can suffer from overconfidence problems [77] . Further-
more, as the upstream DPA-2 LAM and its associated DeePMD-kit platform are in continuous development,
our fine-tuning protocol should keep evolving to harness emerging capabilities. Finally, applying the FT DP
2
modeltomoresimulationtaskswouldbroadenitsutility anddeepeninsightsintothechallengesinthedomain
of iron-based FTS. In the future, we expect to further improve the FT DP model, including using multi-task
2
fine-tuning tactics to resist knowledge loss in unified descriptors, and refining the dataset by active-learning
strategies with suitable uncertainty quantification and unique data selection in order to enrich the dataset for
effectively covering larger configuration space related to the FTS domain from open-source datasets and spe-